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A mass of $2.0\text{ kg}$ is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is negligible. When pressed slightly and released, the mass executes a simple harmonic motion. The spring constant is $200\text{ N/m}$. What should be the minimum amplitude of the motion, so that the mass gets detached from the pan? (Take $g=10\text{ m/s}^2$)
A boy is trying to start a fire by focusing sunlight on a piece of paper using an equiconvex lens of a focal length of $10 \text{ cm}$. The diameter of the sun is $1.39 \times 10^9 \text{ m}$ and its mean distance from the earth is $1.5 \times 10^{11} \text{ m}$. What is the diameter of the sun's image on the paper?
The number of beta particles emitted by a radioactive substance is twice the number of alpha particles emitted by it. The resulting daughter is an:
The intensity at the maximum in Young's double-slit experiment is $I_0$ when the distance between two slits is $d=5\lambda$, where $\lambda$ is the wavelength of light used in the experiment. What will be the intensity in front of one of the slits on the screen placed at a distance $D= 10d$?
The half-life of a radioactive nuclide is 100 hours. The fraction of original activity that will remain after 150 hours would be:
The SI unit of universal gas constant (R) is
At some instant, the number of radioactive atoms in a sample is $N_0$ and after time $t$, the number decreases to $N$. It is found that the graphical representation $\ln N$ versus $t$ along the $y$ and $x$ axis respectively is a straight line. Then the slope of this line is:
The half-life of a radioactive substance is 20 minutes. In how much time, the activity of substance drops to $(1/16)^{th}$ of its initial value?
The ratio of nuclear densities and nuclear volumes of ${}_{26}^{56}\mathrm{Fe}$ and ${}_{2}^{4}\mathrm{He}$ are, respectively:
At any instant, two elements $X_1$ and $X_2$ have the same number of radioactive atoms. If the decay constants of $X_1$ and $X_2$ are $10\lambda$ and $\lambda$ respectively, then the time when the ratio of their atoms becomes $1/e$ will be:
Which one of the following represents forward biased circuit?
Which of the following gate is called the universal gate?
The half-life of radium is 1622 years. How long will it take for seven-eighth of a given amount of radium to decay?
Which one of the following equations of motion represents simple harmonic motion? (where $k, k_0, k_1$ and $a$ are all positive.)
A rectangular block of mass $m$ and area of cross-section $A$ floats in a liquid of density $\rho$. If it is given a small vertical displacement from equilibrium, it undergoes oscillation with a time period $T$. Then:
A particle of mass $m$ is released from rest and follows a parabolic path as shown. Assuming that the displacement of the mass from the origin is small, which graph correctly depicts the position of the particle as a function of time?
A particle executing simple harmonic motion has a kinetic energy of $K = K_0 \cos^2(\omega t)$. The values of the maximum potential energy and the total energy are, respectively:
The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is:
The average velocity of a particle executing SHM in one complete vibration is:
If in a p-n junction, a square input signal of $10\text{ V}$ is applied as shown, then the output across $R_L$ will be: